Problem: s involving definite integrals (algebraic) AP.CALC: CHA‑4 (EU), CHA‑4.D (LO), CHA‑4.D.1 (EK), CHA‑4.D.2 (EK), CHA‑4.E (LO), CHA‑4.E.1 (EK) Google Classroom Facebook Twitter Email You might need: Calculator Problem Water is leaking out of a container at a rate of $-50(t-10)$ milliliters per hour (where $t$ is the number of hours). How many milliliters of water leak out of the container between $t=0$ and $t=2$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $100$ (Choice B) B $400$ (Choice C) C $500$ (Choice D) D $900$
Letting $w(t)$ be the milliliters of water leaked by hour $t$, we are given that $w'(t)=-50(t-10)$. We want to find $w(2)-w(0)$. According to the Fundamental Theorem of Calculus, $\begin{aligned} w(2)-w(0)&=\int_{0}^{2} w'\left(t\right)dt \\\\ &=\int_{0}^{2}\left(-50(t-10)\right)dt \end{aligned}$ $\int_{0}^{2}\left(-50(t-10)\right)dt = 900$ In conclusion, between $t=0$ and $t=2$, approximately $900$ milliliters of water leak out.